Timeline for Estimate for the diameter of the image of a holomorphic disk by the area of the holomorphic disk
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 19, 2021 at 14:23 | comment | added | Shah Faisal | @LeoMoos monotonicity formula will not apply in case the disk u has a thin but long image (big diameter), so the image of u cant be enclosed in a small ball even if u have a very small area. As Alexander pointed out such disks u exist in S^2, thanks LeoMoos, and Alexander for your helpful comments ....... | |
| Apr 18, 2021 at 15:27 | comment | added | Alexandre Eremenko | This is certainly not true. Even when $M$ is the ordinary Riemann sphere, with standard holomorphic structure. You can have a conformal map $D^2\to S$ whose image has arbitrarily small area, and fixed diameter. | |
| Apr 18, 2021 at 14:48 | review | First posts | |||
| Apr 18, 2021 at 14:51 | |||||
| Apr 18, 2021 at 13:50 | comment | added | Leo Moos | I'm not an expert on this, but could the monotonicity formula help? Cf. mathoverflow.net/questions/107468/… | |
| Apr 18, 2021 at 13:20 | history | asked | Shah Faisal | CC BY-SA 4.0 |